Question

Consider these four data sets.

Set A: {1, 4, 6, 8, 2, 3, 9}
Set B: {17, 18, 20, 22, 30, 38, 39, 45, 46, 48}
Set C: {2, 7, 12, 17, 22, 27, 32}
Set D: {12, 32, 24, 15, 16, 28, 39}

The data set that exhibits symmetry is data set: ___

Answer 1

Set C. because every number has a 5 difference between each other.

Answer 2

Answer: Set C is correct answer.

Explanation:

Symmetrical distribution is a type of distribution in which all data occurs at regular frequencies, and the measures of central tendency is occurred at same point.

Here, we can see from the options that

Set C has data with same difference i.e. 5

Here, Median would be 17 as the median is the central value after arranging the data value in ascending order.

Mean =
`(2+7+12+17+22+27+32)/(7)=(119)/(7)=17`

∴ Mean = 17

Mode = 3 Median - 2 Mean

`Mode=3* 7-2* 7\\\\Mode=21-14\\\\Mode=7`

∴ Mode = 7

Thus, all mean, median and mode is occurred at same point i.e. 7.

Hence, Set C is correct answer.